One of the documents Robert Costello provided to CDM.Press evidences that Michael Cohen and Cohen's attorney, Michael Monico, signed a declaration for federal prosecutors in February 2019 representing that Cohen was waiving any claim of privilege from his interactions and conversations with Costello.
"Although I do not believe that any of my communications with Costello or other lawyers at DHC are subject to attorney-client privilege, I hereby waive whatever attorney-client or other privilege that might be argued have attached to such communications," the February 2019 declaration from Cohen's attorney states.
The declaration can be read here:
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